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This paper provides a structural model to value startup companies and determine the optimal level of research and development (R&D) spending by these companies.

This paper describes a new variant of float-the-money options, which can act as a financial instrument for financing R&D expenses for a specific time horizon or development stage, allowing the investor to share in the startup's value appreciation over that duration. Another innovation of this paper is that it develops a structural model for evaluating optimal level of R&D spending over a given time horizon. The paper deploys the Gompertz-Cox model for the R&D project outcomes, which facilitates investigation of how increased level of R&D input can enhance the company's value growth.

The author first introduces a time-varying drift term into standard Black-Scholes model to account for the varying growth rates of the startup at different stages, and the author interprets venture capital's investment in the startup as a “float-the-money” option. The author then incorporates the probabilities of startup failures at multiple stages into their financial valuation. The author gets a closed-form pricing formula for the contingent option of value appreciation. Finally, the author utilizes Cox proportional hazards model to analyze the optimal level of R&D input that maximizes the return on investment.

The integrated contingent claims model links the change in the financial valuation of startups with the incremental R&D spending. The Gompertz-Cox contingency model for R&D success rate is used to quantify the optimal level of R&D input. This model assumption may be simplistic, but nevertheless illustrative.

Once supplemented with actual transaction data, the model can serve as a reference benchmark valuation of new project deals and previously invested projects seeking exit.

The integrated structural model can potentially have much wider applications beyond valuation of startup companies. For instance, in valuing a company's risk management, the level of R&D spending in the model can be replaced by the company's budget for risk management. As another promising application, in evaluating a country's economic growth rate in the face of rising climate risks, the level of R&D spending in this paper can be replaced by a country's investment in addressing climate risks.

This paper is the first to develop an integrated valuation model for startups by combining the real-world R&D project contingencies with risk-neutral valuation of the potential payoffs.

China's population aging is gradually deepening and needs to be actively addressed. The purpose of this paper is to construct a novel model for analyzing the population aging.

To analyze the aging status of a region, this study has considered three major indicators: total population, aged population and the proportion of the aged population. Additionally, the authors have developed a novel grey population prediction model that incorporates the fractional-order accumulation operator and Gompertz model (GM). By combining these techniques, the authors' model provides a comprehensive and accurate prediction of population aging trends in Jiangsu Province. This research methodology has the potential to contribute to the development of effective policy solutions to address the challenges posed by the population aging.

The fractional-order discrete grey GM is suitable for predicting the aging population and has good performance. The population aging of Jiangsu Province will continue to deepen in the next few years.

The proposed model can be used to predict and analyze aging differences in Jiangsu Province. Based on the prediction and analysis results, identified some corresponding countermeasures are suggested to address the challenges of Jiangsu's future aging problem.

The fractional-order discrete grey GM is firstly proposed in this paper and this model is a novel grey population prediction model with good performance.

The purpose of this paper is to present a clear path to securitize the longevity risk with two distinct swaps in order to inspire a new Chinese life market.

Studies on longevity risk securitization consist of three aspects, respectively, instrument design, pricing methodology and mortality projection. The swaps designed are referenced, respectively, to vanilla and complex survivor swaps (Dowd et al., 2006; Lin and Cox, 2005). Methods applied are RHH model and Gompertz law for mortality projection, as well as two-factor Wang transformation for pricing.

This paper figures out the market price of risk in Chinese annuity market, checks for the sensitivity of the price to parameters and tests the hedging effects by Monte Carlo simulation.

Based on the theoretical and numerical results, this paper suggests an effective way to possibly witness the birth of New Life Market in China.

The purpose of this research paper is to underscore that harmonization of laws, much as it might not offer a lasting cure of tax avoidance and other forms of financial crimes, can enhance the fight against it and subsequently help to forestall it. Tax avoidance has remained an intractable challenge and costs governments astronomical sums of money, largely because taxation is a sensitive issue in the realm of sovereign national jurisdictions. The first part of this paper involves a review of empirical data on tax avoidance to create a context for evaluating theoretical issues on tax avoidance and how they are manifested in practice. It draws examples in a cross-jurisdictional perspective given the global character of tax avoidance and evasion as financial crimes. The last part of this paper discusses possible recommendations that could be implemented to tackle tax avoidance and its attendant challenges on economies.

The author has carried out a scoping review of the literature on tax avoidance and myriad of ways used to commit it globally. There was a wealth of data on tax avoidance, evasion, money laundering and harmonization of laws, which was reviewed and applied in undertaking this study. These data were sourced from published academic books, journal articles and online data sources/websites. This paper reflects on and internalizes most recent empirical data on tax avoidance and evasion such as unprecedented leak of millions of files from the database of the world’s fourth biggest offshore law firm, Mossack Fonseca – the so-called “Panama papers”, which has revealed the extent of tax avoidance globally. It also goes an extra length (literally speaking) to underscore important measures that ought to be introduced to address tax avoidance, evasion and money laundering once and for all.

The findings of this paper confirm that while harmonization of law has its inherent shortcomings, it is necessary to enhance individual state’s ability to deal with overlapping interstate challenges such as tax avoidance. This paper proffers a thorough analysis of tax avoidance, the varied context in which it is manifested with a view to evaluate measures that could be adopted by states to minimize or forestall it globally.

This paper has used data on tax avoidance and cognate areas in underscoring inherent challenges in current measures against tax avoidance globally. There were not many studies carried out on the role of harmonization in bolstering states’ efforts against tax avoidance and other financial crimes.

Paying taxes or avoiding paying it has a direct bearing on people, societies and national governments. It is therefore important that states adopt measures to curtail tax avoidance – because it costs governments a lot of revenue.

Though studies have been conducted on tax avoidance and cognate areas, this paper articulates that harmonization could greatly enhance the fight against it globally. This paper will appeal to tax authorities, banks, governments, policy makers, oversight financial institutions and those who have a vested interest in regulation of financial crimes globally.

The purpose of this paper is to propose a model for ruin‐contingent life annuity (RCLA) contracts under a jump diffusion model, where the dynamics of volatility is governed by the Heston stochastic volatility framework. The paper aims to illustrate that the proposed jump diffusion process, for both asset price and stochastic volatility, will provide a more realistic pricing model for RCLA contracts in comparison to existing models.

Under the assumption of the deterministic withdrawals, the authors use a partial integro differential equation (PIDE) approach to develop the pricing scheme for the fair value of the lump sum charges of RCLA contracts. Consequently, the authors employ an elegant numerical scheme, finite difference method, for solving the PIDEs for the reference portfolio, as well as the volatility. The findings show that a different pricing behaviour of the RCLA contracts under the authors' model parameters is obtained compared to that in the existing literature.

RCLA pricing in the complete market often underestimates the jump risk and the persistent factor in the volatility process. The authors' generalized model shows how these two random sources of risks can be precisely characterized.

The parameter values used in the numerical analysis require more empirical evidence. Hence, in order for more precise pricing practice, the calibration from real data is needed.

The model, as adopted in this study, for pricing of RCLA contracts should provide a general guideline for the commercialization of this product by insurance companies.

The demand for RCLA contracts as an alternative to the commonly‐practised annuitization option has recently increased, rapidly, among the soon‐to‐retire baby boomers. This paper investigates the fair value of this particular product, which could be beneficial to researchers for a better understanding of the product design.

This is the first research paper which prices the RCLA contracts in the incomplete market. The gap between RCLA contract pricing and studies of jump diffusion models for derivative pricing, in the literature, is therefore filled.

The theory of competitiveness of cities is based on Porter’s Diamond Theory. There is a relation between housing and urban competitiveness. The adequacy of land supply and allocation of land for new housing development is integral. This paper aims to estimate the required number of housing units to secure housing needs in Tehran for the next four years in 1400 H.Sh (2021 A.D.). The research methodology is carried out using qualitative and quantitative approaches based on the given data. First, the population of Tehran in 1400 H.Sh was predicted using nonlinear quadratic polynomial, Gompertz and logistic models. Then, a Logistic model is proposed to estimate the number of housing units in Tehran. The calculations of residential units related to the population obtained from the Gompertz model equivalent to 663141 is suggested as a criterion for local authority to future decision making and planning for urban development.

The present research is an applied research in terms of the purpose a descriptive research in terms of the nature and methodology and a descriptive-analytical research in terms of attitude and approach toward the research problem (Hafeznia, 2013, 58, 63 and 71). To provide the required information for the analytical stage, a documentary method, related to the use of internal and external books and papers, has been applied. First, the population of Tehran in 1400 H.Sh is estimated using three nonlinear models of quadratic polynomials, Gompertz and logistic. Then, among them, the options that were more consistent with the estimation of the new comprehensive plan of Tehran (1386 H.Sh), which is the most important plan of this city, were chosen. After that, by using the logistic model, which is an appropriate expression of saturable phenomena and a suitable method of estimating the number of residential units in a city and based on the past trend, the future of housing is predicted, and the number of required residential units is determined.

Any city for competitiveness must seek the search and development of a set of unique strategies and practices that will shape its status from other cities. No single action for all cities is feasible. In fact, the most important challenge is to propose a unique value proposition and to formulate a strategy that distinguishes that city from the rest. Among the measures taken around the world is attention to infrastructure. From the point of view of competitiveness, different types of investment in infrastructure are important for different types of cities and in different stages of development of a city. Large cities need targeted investments in housing issues to overcome the segments associated with the poorer neighborhoods. Without investment in desirable housing, there will be holes in competitive advantage. In this paper, the number of residential units in Tehran was projected for 2021. The city’s population was originally estimated for 2021. In addition to the models used to predict and estimate necessary, it is necessary to consider the area, land use map, future development lines and […] city. To this end, the city can continue to meet the needs of residents’ diversification and the city’s needs. We cannot accept any predictions about the population and, consequently, the number of residential units. Providing predictions can provide the most predictive, or more prudent, and different scenarios that can emerge, which will lead to flexibility in the presentation of plans and programs. Among the models that were used to predict the population, the result obtained from second-order polynomial and Gompartz models was found to be appropriate for the estimation of the new comprehensive design of Tehran (2007). But the prediction of the population of the logistic model was beyond the prediction of the new comprehensive plan of Tehran (2007) and thus was not considered appropriate. The number of residential units required according to the predicted population of the second order polynomial models, Gompartz and the population considered in the new comprehensive plan of Tehran (2007). After the finalization of the proposed population, using the logistic model, the number of residential units needed in Tehran was projected for 2021. Since these three estimates are somewhat close to each other, it is suggested that Gompertz model calculations, equivalent to 663,141 residential units, are proposed, and according to that, local authorities are planning to supply land to achieve economic competitiveness (urban). As it is shown in the conceptual model of the paper in Figure 1, after determining the need for housing, it is necessary to ask whether the adequacy of the supply and allocation of land, as well as the importance of maintaining it for the development of housing by local authorities, is clear. Also, is there any suitable planning for that? Despite the severe shortage of ready-made land for the city of Tehran, a large volume of land is a large area owned by natural and legal persons, and, in particular, state-owned enterprises of semipublic and public institutions, which have been abandoned in cities for years without use and in the form of barren. According to municipal management laws, municipalities can receive land, taxes and fees that are included in the annual budget of the Tehran Municipality. According to the figure obtained from this study, which states that 663,141 residential units are needed for Tehran in 2021, large landowners in Tehran need to supply their land to the market. According to the Population and Housing Census in Tehran in 2011, there are 245,769 inhabited vacancies in Tehran; hence there are two scenarios for the provision of residential units in the city of Tehran in 2021, assuming that these units in the housing market require 417,372 units Another residence will be for Tehran, otherwise 663141 residential units will be needed for Tehran in 2021. Other possibl

Tehran is the largest city and the capital of Iran, and it is also the capital of the province Tehran. In the southern foothills of the Alborz Mountains within a longitude of 51 degrees and 2 minutes East to 51 degrees and 36 minutes East, with an approximate length of 50 kilometers and latitude 35 degrees and 34 minutes North to 35 degrees and 50 minutes North with an approximate width of 30 kilometers. The area of this city is 730 km². This is one of the largest cities in West Asia, the 25th the most populous city, and the 27th greatest city to the world. The administrative structure of Iran has been concentrated in this city. The city has been divided into 22 zones, 134 areas (including Rey and Tajrish), and 370 districts (Wikipedia). The problem of housing in the city of Tehran has always been one of the important issues that less has been planned for it. The result is housing shortage, high housing prices and so on, due to the excessive expansion of the city, its population increase and so on.

Motivated with the ever growing number of bibliometric trend extrapolation studies, the purpose of this paper is to demonstrate through two technologies how the selection of an upper limit of growth affects the correlation and causality of technology development measured with bibliometric data.

The paper uses Gompertz and Fisher-Pry curves to model the technological development of white light emitting diodes and flash memory, and show with extrapolation results from several bibliometric sources how a typical bias is caused in trend extrapolations.

The paper shows how drastic an effect the decision to set an upper bound has on trend extrapolations, to be used as a reference for applications. The paper recommends carefully examining the interconnection of actual development and bibliometric activity.

Despite increasing interest in modelling technological data using this method, reports rarely discuss basic assumptions and their effects on outcomes. Since trend extrapolations are applied more widely in different disciplines, the basic limitations of methods should be explicitly expressed.

The purpose of this paper is to establish an exponentially weighted moving average (EWMA) control chart for monitoring the mean level of Gompertz lifetimes with type‐I censoring.

The proposed control chart is developed based on the conditional expected values (CEVs). The control limits are determined numerically with an algorithm.

Compared with the EWMA CEV control charts of Zhang and Chen, numerical results indicate that the proposed control chart has good performance to detect mean shifts for Gompertz lifetimes either in decrease or in larger increase with type‐I censoring in terms of the average run length (ARL).

The paper shows that, based on the proposed method, practitioners can monitor the mean level of Gompertz lifetimes via an EWMA CEV control chart with type‐I censoring.

The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter.

The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples.

Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known.

Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

Several studies find that there is little sex gap in wages at labor market entry, and that the sex gap in wages emerges (and grows) with time in the labor market. This evidence is consistent with (i) there is little or no sex discrimination in wages at labor market entry, and (ii) the emergence of the sex gap in wages with time in the labor market reflects differences between women and men in human capital investment (and other decisions), with women investing less early in their careers. Indeed, some economists explicitly interpret the evidence this way. We show that this interpretation ignores two fundamental implications of the human capital model, and that differences in investment can complicate the interpretation of both the starting sex gap in wages (or absence of a gap), and the differences in “returns” to experience. We then estimate stylized structural models of human capital investment and wage growth to identify the effects of discrimination (or other sources of a starting pay gap) and differences in human capital investment.